Mathematical ecology

This is an introductory textbook on mathematical ecology bridging the subdisciplines
of population ecology and ecosystem ecology. The expected reader is you: a beginning
graduate student, advanced undergraduate student, or someone who thinks of
themselves as a student all their lives, with a working knowledge of basic calculus
and basic ecology. While this is intended as a stand-alone text, the level is such that
once you have read through it, you will be able to read more advanced texts and
monographs such as Ågren and Bosatta (1998) and Kot (2001) with greater depth.

The epidemiology of infectious diseases is one of the great triumphs of applied
ecology. In particular, the public health importance of parasites has
lead to a large literature, exploring their impact on the population dynamics,
population genetics and evolutionary biology of human populations. An
important milestone was the Dahlem Conference on population biology of infectious
diseases, held in 1981. The resulting book (Anderson and May 1982)
lucidly summarised the contemporary state of parasite ecology and epidemiology.

The 8th International Congress of Ecology was held in Seoul, South Korea in
August 2002, and was hosted by the Ecological Society of Korea. The Congress
theme was 'Ecological Issues in a Changing World', and this volume includes
selected contributions to illustrate some of the important topics which were
discussed during the Congress.
Problems of scale have exercised the minds of ecologists for many years, and
will continue to do so into the future. This volume deals with this subject and with
mathematical approaches to improve our understanding of complex ecological
systems.

The scope of this book is to demonstrate that we do have an ecosystem theory that can be
used to describe ecosystem structure and function. It was previously shown in the book,
Integration of Ecosystem Theories: A Pattern (3rd edition, 2002), that the various contributions
to systems ecology are consistent and together form a pattern of ecological
processes. My book with Yuri Svirezhev, Toward a Thermodynamic Theory of Ecosystems
(2004), presented the thermodynamics of this pattern in a mathematical language....

The second section of the book involves the regional biogeography of individual taxa.
This section begins with a chapter by Alberto Taylor and his colleagues on the
biogeography of cycads in Central America. Their natural history and experimental
ecological methods integrate the evolutionary context of the cycad lineage with
contemporary autecology, and they elucidate biogeographic patterns and conservation
priorities, the latter of which are under-appreciated but pressingly important in
Central America.

Suppose we have a function f (x) where the variable x may be a vector of many
dimensions. We seek the point x∗ such that f (x∗) is the maximum value among
all possible f (x). This point x∗ is called the global optimum of the function f (x).
It is possible that x∗ is a unique point but it is also possible that there are several
points that share the maximal value f (x∗). Optimization is a field of mathematics
that concerns itself with finding the point x∗ given the function f (x).

Dynamical systems theory in mathematical biology and environmental science
has attracted much attention from many scientific fields as well as mathematics.
For example, “chaos” is one of its typical topics. Recently the preservation
of endangered species has become one of the most important issues
in biology and environmental science, because of the recent rapid loss of
biodiversity in the world. In this respect, permanence or persistence, new
concepts in dynamical systems theory, seem important.

Nowadays, environmental issues including air and water pollution, climate
change, overexploitation of marine ecosystems, exhaustion of fossil resources,
conservation of biodiversity are receiving major attention from the public,
stakeholders and scholars from the local to the planetary scales. It is now
clearly recognized that human activities yield major ecological and environ-
mental stresses with irreversible loss of species, destruction of habitat or cli-
mate catastrophes as the most dramatic examples of their eﬀects.

In the sea medium, the accumulation of organisms can be observed at the water–solid
body interface. Biomasses developing on hard surfaces often exceed those on softground
bottom communities by tens and hundreds of times. Such a concentration
of organisms points to their ecological and economic significance.

As a premise to this textbook on Numerical ecology, the authors wish to state their
opinion concerning the role of data analysis in ecology. In the above quotation, Goethe
cautioned readers against the use of mathematics in the natural sciences. In his
opinion, mathematics may obscure, under an often esoteric language, the natural
phenomena that scientists are trying to elucidate. Unfortunately, there are many
examples in the ecological literature where the use of mathematics unintentionally lent
support to Goethe’s thesis.

Dynamical systems theory in mathematical biology and environmental science
has attracted much attention from many scientific fields as well as mathematics.
For example, “chaos” is one of its typical topics. Recently the preservation
of endangered species has become one of the most important issues
in biology and environmental science, because of the recent rapid loss of
biodiversity in the world. In this respect, permanence or persistence, new
concepts in dynamical systems theory, seem important.

Unfortunately many people do not value their health until they lose it. It can be reasoned
however that if people can understand and appreciate better the basis of human value
systems they could be more likely to reappraise their values and thereby encouraged to
address aspects of life and living which have more intrinsic and sustainable or ‘real’ value
for them.

This paper was presented as the first annual John Gerhart Memorial Lecture at the conference of the Africa Genome Initiative held in Cairo in March 2004. In Africa in the Age of Biology, Dr James discusses Africa’s long history of scientific, technological and mathematical enterprise, from tokens of the very earliest counting by humans to the sum of knowledge brought to bear in the construction of the pyramids. But he focuses on the challenges of today, and tomorrow, which he suggests Africa’s leaders and scholars dare not overlook....

Important factor in political decision-making is a public opinion as well. Therefore, it is very important to raise global ecological awareness and wider public education regarding ecology. Goal of this book is to bring closer to the readers new drive technologies that are intended to environment and nature protection. The book presents modern technique achievements and technologies applied in the implementation of electric vehicles. Special attention was paid to energy efficiency of EV's. Also today's trends, mathematical models and computer design elements of future cars are presented....

What makes populations stabilize? What makes them fluctuate? Are populations in complex ecosystems more stable than populations in simple ecosystems? In 1973, Robert May addressed these questions in this classic book. May investigated the mathematical roots of population dynamics and argued-counter to most current biological thinking-that complex ecosystems in themselves do not lead to population stability.

Modern game theory has evolved enormously since its inception in the 1920s in the
works of Borel and von Neumann. The branch of game theory known as dynamic
games descended from the pioneering work on differential games by R. Isaacs,
L. S. Pontryagin and his school, and from seminal papers on extensive form games
by Kuhn and on stochastic games by Shapley.